You are pretending that no character can be created, outside of the player's ability to interpret it. You are removing the concept of territory, by suggesting that the map is the only thing that matters. That's not how the brain works. There must be a territory upon which we base our map, even if that territory only exists in our collective imagination.
When you play a role, you imagine yourself in the position of the character. You imagine yourself as that character in that same situation, and whatever you decide you would do, that is how you know what the character would do.
Someone else could try to play the same role, though. (Imagine that you're sick that week, so your friend takes over your character.) She could imagine herself as that character in that situation, and decide what the character would do. She might decide that the character does the same thing that you would have decided, had you been there, or she might decide that it does something else. This is possible because the character exists outside of our playing it. It is a real part of that world, by mutual consensus. If there wasn't a territory of the character, upon which she could base her map, then it would be impossible for her to play that character. If she decided to do something which is not a reasonable interpretation of what that character would do, then she would be playing the role poorly.
Given that this is a role-playing game, poor role-playing should be avoided when possible.